Precision pole estimation methods are currently used in a wide variety of fields, such as DNA structural analysis in nuclear magnetic resonance spectroscopy (NMR) (see, for example, Murata, Kubota, “Precision Pole Estimation Method Based on AR Process and an Application to the NMR Structural Analysis”, IEICE A, Vol. J91-A, No. 8, pp. 772-781, August 2008).
Plans are in the works to launch and operate extremely small satellites called “nano-satellites” at much lower cost than conventional satellites, and disturbance component analysis of attitude control signals for nano-satellites is one of the fields in which precision pole estimation methods are used.
Because nano-satellites are artificial satellites of an unprecedented small size, attitude control plays an important role in observation precision, and these controls have to be performed adaptively. Because the orbital altitude is also lower than before, the disturbances from the natural environment are also different, and the effects of residual magnetic torque are much higher (see, for example, T. Inamori, N. Sako, S. Nakasuka, “Attitude Control System For the Nano-Astrometry Satellite Nano-JASMINE”, International Journal of Aircraft Eng. and Aerospace Technology, pp. 221-228, 2011). This means disturbance factors related to observation results include a closed-loop control system that is an adaptive system with very short times, and plant impacts that cannot be assumed based on experience with conventional artificial satellites. Usually, external disturbances affecting artificial satellites pose difficult problems for low-frequency band signals.
In the prior art, as described, for example, in Japanese Laid-open Patent Publication No. 2000-224077 and Japanese Laid-open Patent Publication No. 2008-199602, controls and observations are performed based on the assumption that all disturbances are white Gaussian signals. However, actually, the low SN ratio signals mentioned above have many unknown frequency signals (multi-tone signals) embedded in the noise. If low SN ratio multi-tone signals are whitened or transformed to a level of disturbance that can be disregarded via modeling and reverse filtering, control and observation precision can be improved. Therefore, an effective technique is required for this modeling.
Identifying an observation signal system as an auto-regressive (AR) model and then applying a reverse filter of this is believed to be effective. In the case of the precision estimations described in Non-patent Literature 1, the effect is often weak on disturbances. However, a technique has been proposed in which an estimation of the number of sine waves is performed based on eigenvalue distributions, etc. even when the SN ratio is negative (see, for example, Tsuji, Ohmori, Sano, “Determination of Number of Sinusoidal Signals in AR Spectral Estimation,” IEICE A, Vol. J74-A, No. 9, pp. 1374-1384, September 1991), but this differs from a parameter estimation that is able to configure a spectrum envelope.
Therefore, what is needed for nano-satellite control is automatic precision estimation in which there is bias in the pole distribution based on a low SN ratio at a level for configuring a reverse filter, that is, based on observation signals of several dB, and in which the pole spectrum envelope is not destroyed.